A fixed‐mesh Eulerian–Lagrangian approach for stress analysis in continuous casting

Abstract

SUMMARYWe present a method for the analysis of the strains and stresses developed in the solidified portion of a metal strand during the continuous casting process. Steady-state conditions are assumed. The solidified metal is modelled as a standard inelastic solid with isotropic hardening and von Mises yield criterion. Constitutive equations are formulated over the material particles (Lagrangian approach) that instantaneously occupy a fixed domain attached to the casting machine, which is discretized (Eulerian approach). Particle tracking, needed to record the deformation history at each fixed sampling point, becomes trivial because of the usual hypothesis of constant and homogeneous advection velocity. Backward-Euler (implicit) finite differences and mixed finite elements are used for time and spatial discretization, respectively. The resulting non-linear algebraic equations are solved using the Newton-Raphson method.

Element-Free Galerkin Formulation by Moving Least Squares for Internal Energy Balance in a Continuous Casting Process

“…Even today, several researchers are still conducting studies based on 1‐D pseudo‐transient models in order to analyze more specific issues regarding the CC process, such as: the convective heat transfer at the solid–liquid interface, and the convective coefficient for the Robin cooling condition through the solution of a mold‐slab coupled heat transfer problem . On the other hand, in the longitudinal section approach, the domain analysis implies explicitly the whole region of interest from the meniscus until the mold outlet, which results in a more accurate computation of boundary conditions and material properties . Therefore, in process whose boundary conditions and particularly temperature change markedly, the cross‐section slice models have been replaced for longitudinal‐section models under Lagrangian, Eulerian–Lagrangian, and purely Eulerian approaches, due to accuracy and computation time considerations.…”

“…Therefore, in process whose boundary conditions and particularly temperature change markedly, the cross‐section slice models have been replaced for longitudinal‐section models under Lagrangian, Eulerian–Lagrangian, and purely Eulerian approaches, due to accuracy and computation time considerations. This is particularly so in the case of wide slabs and round billets problems, where plain and axisymmetric temperature and displacements assumptions exhibit satisfactory results . However, it should be noted that all these models have been solved by using only mesh‐based methods.…”

Thermal stress evaluation in the steel continuous casting process

“…In Section 2.2, we present an alternative Eulerian-Lagrangian procedure where no EPSC condition is assumed (see References [22,23]). Section 4 presents a comparative analysis of results obtained with both models for the simulation of a billet continuous casting process.…”

Efficient thermo-mechanical model for solidification processes

“…The Euler backward method of integration is used to convert the system of ODEs at each material point, Equation (14), to the following equation system:…”